Home
Class 12
MATHS
Prove that for any two numbers x1 and x2...

Prove that for any two numbers `x_1` and `x_2.(2e^(x_1)+e^(x_2))/3gte^((2(x_1)+x_2)/3)`

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Evaluate int(e^(2x)-2e^(x))/(e^(2x)+1)dx

int (e^(4x)-2e^(3x)+5e^(x)-2)/(e^(x)+1)dx

int e^(x).(x^(2)+1)/((x+1)^(2))dx

int e^(x)((1-x)/(1+x^(2)))^(2)dx

Prove that, underset(x to 0) lim ((1+6x^(2))/(1+2x^(2)))^(1/x^(2))=e^(4)

Evaluate : int (e^(2x-1)-e^(1-2x))/(e^(x+2)) dx

Integrate : int (e^(x) dx)/(1-3e^(x)-3e^(2x))

int(e^(x)(1+x^(2)))/((1+x)^(2))dx

Prove that: underset(x rarr0)lim ((x-1+cosx)/(x))^(1/x) = e^(-1/2)

Find (dy)/(dx) : y =2^(x+2)-e^(x+1)+3log_(e) x

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Let f(x)=x^3+a x^2+b x+5sin^2x be an increasing function on the set Rd...

    Text Solution

    |

  2. Find the possible values of a such that f(x)=e^(2x)-(a+1)e^x+2x is mon...

    Text Solution

    |

  3. Prove that for any two numbers x1 and x2.(2e^(x1)+e^(x2))/3gte^((2(x1)...

    Text Solution

    |

  4. Assertion Consider the following statements in SandR S: Both sinx and...

    Text Solution

    |

  5. Let f(x)=int0^xe^t(t-1)(t-2)dt, Then f decreases in the interval

    Text Solution

    |

  6. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  7. Tangent is drawn to ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costheta,sint...

    Text Solution

    |

  8. If f(x)=xe^(x(1-x)) , then f(x) is(a) increasing on [−1/2,1] (b) decr...

    Text Solution

    |

  9. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x) as b...

    Text Solution

    |

  10. Suppose that f is a polynomial of degree 3 and that f^(x)!=0 at any...

    Text Solution

    |

  11. The maximum value of the function f(x)=((1+x)^(0. 6))/(1+x^(0. 6)) in ...

    Text Solution

    |

  12. The value of a for which the functionf(x)=asinx+1/3sin3x has an extrem...

    Text Solution

    |

  13. If f(x)=(t+3x-x^2)/(x-4), where t is a parameter that has minimum and ...

    Text Solution

    |

  14. A factory D is to be connected by a road with a straight railway line ...

    Text Solution

    |

  15. Let f(x)=ax^3+bx^2+cx+1 has exterma at x=alpha,beta such that alpha ...

    Text Solution

    |

  16. Consider the function f(x)=xcosx-sinxdot Then identify the statement w...

    Text Solution

    |

  17. The number of values of k for which the equation x^3-3x+k=0 has two di...

    Text Solution

    |

  18. The least natural number a for which x+a x^(-2)>2AAx in (0,oo) is 1 (b...

    Text Solution

    |

  19. A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...

    Text Solution

    |

  20. A rectangle of the greatest area is inscribed in a trapezium A B C D ,...

    Text Solution

    |